How much genetic variation can be maintained by genotype-environment interactions?

In a recent paper by GILLESPIE and TURELLI (1 989), the authors suggest a model of genotype-environment interactions in which the contribution of a particular allele to a quantitative character depends on the environment. Based on this model, they come to the conclusion that such mechanism " may be a potent force maintaining genetic variation in quantitative characters. " The purpose of this note is to show this conclusion not warranted. The authors claim the following result for their model: the variance (across all environments) of the " genotype-specific " environmental component, VZC, associated with a particular genotype depends solely on the degree of heterozygosity and is an increasing function of the number of homozygous loci in the genotype, i.e., for an m-locus genotype, (1) where a superscript indicates the number of homozy-gous loci. The authors assert further that condition (1) implies that under stabilizing selection the fitness of a genotype (averaged across all environments) also depends solely on the degree of heterozygosity and is a decreasing function of the number of homozygous loci, i.e., It has been demonstrated by KARLIN (1979) that a symmetric multilocus genetic system with such fit-nesses has a stable central polymorphism with all al-leles maintained at high frequencies. This, state the authors, proves that their model can result in " the maintenance of very large amounts of genetic variation. " The result concerning the ordering of the " genotype specific " variances (1) is, indeed, correct, albeit under important symmetry assumptions imposed on the model (see a discussion below). It does not necessarily imply, however, condition (2) for the fitnesses. The authors derive (2) and, hence, prove the existence of a stable polymorphism with high allelic frequencies by using the " limiting argument, " i.e., assuming that " the contributions of each allele are very small. " It is important to realize, however, that high allelic frequencies do not automatically result in high genetic variation. The genetic variance is determined not only by allelic frequencies but by the differences in the genotypic values between genotypes as well. If all genotypes have similar genotypic values, the amount of genetic variation in a population will always be small, no matter how high the allelic frequencies can be. Since under the limiting argument the allelic contributions are assumed absolutely small (approaching zero) rather than relative to the total contributions by all alleles from all loci, differences between genotypic …